Find the Derivative - d/dx (3x-2)^2

Problem

d(3*x−2)/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, where the outer function is u2 and the inner function is u=3*x−2

2. Apply the Power Rule to the outer function by bringing the exponent to the front and decreasing the power by one.

d(3*x−2)/d(x)=2*(3*x−2)(2−1)⋅d(3*x−2)/d(x)

3. Differentiate the inner function 3*x−2 with respect to x

d(3*x−2)/d(x)=3

4. Multiply the results together to find the derivative.

2*(3*x−2)1⋅3

5. Simplify the expression by multiplying the constants.

6*(3*x−2)

6. Distribute the constant into the binomial.

18*x−12

Final Answer

d(3*x−2)/d(x)=18*x−12

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